It is well-known that a transducer used in a device satisfying the above definition has an axis, in the mathematical meaning of the word, which may be termed the main axis, and that the signal it produces is a measure of its angular speed about this main axis or, in other words, of the projection on this main axis of the vector representing its angular speed.
Further, such a device is obviously intended to measure, in fact, the angular speed of an object to which this transducer is secured.
In order not unduly to complicate the following description, use will be made therein of the expression "angular speed of the transducer" to designate the angular speed (or velocity), about the above-mentioned main axis, of the object to which this transducer is secured.
U.S. Pat. No. 4,899,587, for instance, describes a transducer that can be used in such a device.
This transducer comprises two tuning forks having a common base which are chemically etched, along with the base, in a thin plate of Z-cut quartz such that the longitudinal axis of the tuning forks is substantially parallel to the Y, or mechanical, axis of the quartz. Electrodes for exciting a first vibration of the transducer are arranged on the prongs of one of the tuning forks so as to cause an alternating and periodic flexing of these prongs in the plane of the transducer when they receive an exciting signal E from a suitable electronic circuit.
The two tuning forks being mechanically coupled by their common base, the prongs of the second tuning fork also undergo an alternating and periodic flexing in the plane of the transducer in response to exciting signal E.
When the exciting signal E is applied to the transducer, and the latter is rotated about an axis parallel to the longitudinal axis of the tuning forks, the prongs of the latter are subjected to the Coriolis force resulting from this rotation. This Coriolis force modifies the transducer's vibration which can then be considered as being formed by the superposition of the first vibration described above and of a second vibration consisting of a flexing vibration of the tuning forks prongs in a direction perpendicular to the plane of the transducer.
Detection electrodes are arranged on the prongs of the second tuning fork of the transducer to produce a detection signal D in response to this second vibration.
U.S. Pat. No. 4,899,587 discloses no circuit able to process this detection signal D to produce a measurement signal of the angular speed of the transducer.
U.S. Pat. No. 4,671,112, which describes another type of transducer that can be used in an angular speed measuring device, describes also a circuit that could be used to produce a measurement signal of the angular speed of the transducer in U.S. Pat. No. 4,899,587, or any other transducer intended for the same use.
This circuit includes a conventional mixing circuit, which mixes a first signal P having an amplitude that is proportional to the amplitude of detection signal D with a second signal, called reference signal F, having an amplitude that is proportional to the amplitude of exciting signal E.
In this circuit, the mixed signal produced by this mixing circuit is filtered by a low-pass filter which suppresses its ac component and only allows its dc component through, the latter being then amplified by a dc amplifier which issues on its output a measurement signal of the angular speed of the transducer. This latter signal will hereinafter be called signal M in the description.
To simplify the considerations that will follow, it will be assumed that signals E, F, D and P are sinusoidal, that signal F is in phase with signal E and that signal P is also in phase with signal D.
Under these conditions, signal E may be expressed by equation: EQU E=E.sin .omega.t (1)
in which E and .omega. respectively are the amplitude and the angular frequency of signal E, and signal F may be expressed by equation: EQU F=K1.E.sin .omega.t (2)
in which K1 is the gain of the circuit that produces signal F from signal E.
As is also well-known, detection signal D includes a first component which consists of the signal that appears across the detection electrodes of the transducer when the angular speed of the latter is zero, and a second component which consists of the signal that superposes itself on this first component when the transducer's angular speed is not zero.
The first component of signal D, hereinafter termed component D.sub.1, may be expressed by equation: EQU D1=D.sub.1.sin (.omega.t+.phi..sub.1) (3)
in which D.sub.1 and .phi..sub.1 respectively are the amplitude of component D.sub.1 and its phase-shift in relation to exciting signal E, these two terms being constant and being dependent only on the transducer being used but not, of course, on its angular speed.
The second component of signal D, hereinafter termed component D.sub.2, may be expressed by equation: EQU D.sub.2 =D.sub.2.sin (.omega.t+.phi..sub.1 +.phi..sub.2) (4)
in which D.sub.2 and .phi..sub.2 respectively are the amplitude of component D.sub.2, which depends on the transducer s angular speed, and the phase shift of component D.sub.2 in relation to component D.sub.1, which is also constant and independent of the transducer's angular speed.
Signal D, which consists of the superposition of its components D.sub.1 and D.sub.2, is thus expressed by equation: EQU D=D.sub.1.sin (.omega.t+.phi.1)+D.sub.2.sin (.omega.t+.phi.1+.phi.2)(5)
The above-mentioned signal P may thus be expressed by equation: EQU P=K2.[D.sub.1.sin (.omega.t+.phi.1)+D.sub.2.sin (.omega.t+.phi.1+.phi.2)](6)
in which K2 is the gain of the circuit that produces signal P from signal D.
As mentioned earlier, signals F and P are mixed and the signal resulting from this mixing is filtered by a low-pass filter that only lets through its dc component, the latter being finally amplified by a dc amplifier that delivers measurement signal M.
It will readily be seen that, under these conditions, signal M is expressed by equation: EQU M=K3.]D.sub.1.cos.phi.1 +D.sub.2.cos(.phi..sub.1 +.phi..sub.2)](7)
in which K3 is equal to the product of gains K1 and K2 mentioned earlier, of the low-pass filter's gain, of the dc amplifier's gain, and of a factor 1/2 that stems from the calculation of equation (7) from equations (1) and (6).
As already stated, the amplitude D.sub.1 of the component D.sub.1 of signal D and the phase-shifts .phi..sub.1 and .phi..sub.2 defined above depend only on the transducer being used and not on the angular speed of the latter, the only factor that is dependent on this angular speed in equation (7) therefore being the amplitude D.sub.2 of the component D.sub.2 of signal D.
Signal M thus comprises a constant component Ml which is represented by the term K3.D.sub.1.cos.phi..sub.1 of equation (7), and a component M.sub.2 that varies in dependence on the transducer's angular speed and which is represented by the term K3.D.sub.2.cos(.phi..sub.1 +.phi..sub.2) of equation (7).
Now, in a first approximation, the phase-shift .phi..sub.1 is zero because the transducer's vibration that creates the component D.sub.1 of signal D is in phase with the vibration caused by exciting signal E. Further, still in a first approximation, the phase-shift .phi..sub.2 is equal to .pi./2 since, when the transducer's angular speed is not zero, the elongation of each point of the transducer which vibrates in the vibration that creates the component D.sub.2 of signal D is proportional to the Coriolis force being applied on the transducer, this Coriolis force is proportional to the speed of this point in the vibration that creates the component D.sub.1 of signal D, and this speed is phase-shifted by .pi./2 in relation to the elongation of this point in this latter vibration, which elongation is of course in phase with the exciting signal E.
In this first approximation, signal M is therefore independent of the transducer's angular speed since the factor cos (.phi..sub.1 +.phi..sub.2) of the component M.sub.2 of signal M is equal to zero.
In practice, the phase-shifts .phi..sub.1 and .phi..sub.2 are generally slightly other than zero and .pi./2, respectively, because of the transducer's mechanical losses.
The factor cos (.phi..sub.1 +.phi..sub.2) of the component M.sub.2 of signal M is therefore not zero, and this signal M can therefore actually vary in dependence on the transducer's angular speed.
But this factor cos (.phi..sub.1 +.phi..sub.2) is always very small since the sum of the phase-shifts .phi..sub.1 +.sub.2 is close to .pi./2 so that the component M.sub.2 of signal M is always much smaller than component M.sub.1 unless the transducer's angular speed and hence the amplitude D.sub.2 of the component D.sub.2 of signal D are very large.
Clearly, the circuit described in U.S. Pat. No. 4,671,112 cannot properly be used in a device for measuring a relatively small angular speed because the signal M it produces then essentially consists of a component M.sub.1 that is independent of this angular speed on which is superposed a component M.sub.2 of low, or even very low, amplitude in relation to that of component M.sub.1. Such a signal M is in practice difficult to use.
It should be noted that this same drawback occurs with all circuits of the kind described in U.S. Pat. No. 4,671,112, i.e. circuits which mix, in one way or another, a signal that is produced directly or indirectly by the transducer's detection electrodes with a signal that is derived from the exciting signal of the transducer.
In other words, the sensitivity of angular speed measuring devices using such circuits is low.
Further, the presence in such circuits of analog amplifiers whose components have characteristics able to vary with respect to time and/or temperature means that the signal M that is produced by these circuits also varies with respect to these parameters. Signal M is therefore not stable.
It is of course conceivable to complete this kind of circuit with a circuit capable of subtracting from signal M a constant compensatory signal equal to the component M.sub.1 of signal M so as only to retain the useful component M.sub.2 of signal M, and to amplify as much as is necessary the signal resulting from this subtraction.
But the amplitude D.sub.1 and the phase-shift .phi..sub.1 of the component D.sub.1 of signal D can vary from one transducer to the next even with transducers of the same type. The production of the above mentioned compensatory signal therefore implies not only having to measure amplitude D.sub.1, something that does not in general give rise to any particular difficulty, but also having to measure phase-shift .phi..sub.1, a far trickier operation since this phase-shift is very close to zero. Moreover, the characteristics of the components of the circuit that produces this compensatory signal and that cause the latter to be subtracted from signal M may also vary with respect to time and/or temperature, thereby reducing still further the stability of measurement signal M.
An object of the present invention is to propose an angular speed measuring device that does not suffer from the above drawbacks, i.e. that supplies a measurement signal that is stable and readily usable regardless of the transducer being used and of the latter's angular speed.